scholarly journals Investigation on linear and nonlinear dynamic equation for vehicle model in numerical simulation

2021 ◽  
Vol 1078 (1) ◽  
pp. 012010
Author(s):  
Li Maoqi ◽  
M I Ishak ◽  
P M Heerwan
Keyword(s):  
Numerical Simulation ◽  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Vehicle Model ◽  
Nonlinear Dynamic Equation ◽  
Linear And Nonlinear

scholarly journals Oscillation Criteria of Singular Initial-Value Problem for Second Order Nonlinear Dynamic Equation on Time Scales

2018 ◽  
Vol 5 (1) ◽  
pp. 102-112 ◽  
Author(s):  
Shekhar Singh Negi ◽  
Syed Abbas ◽  
Muslim Malik
Keyword(s):  
Time Scales ◽  
Initial Value Problem ◽  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Type Inequality ◽  
Second Order ◽  
Oscillation Criterion ◽  
Initial Value ◽  
Nonlinear Dynamic Equation ◽  
Singular Initial Value Problem

AbstractBy using of generalized Opial’s type inequality on time scales, a new oscillation criterion is given for a singular initial-value problem of second-order dynamic equation on time scales. Some oscillatory results of its generalizations are also presented. Example with various time scales is given to illustrate the analytical findings.

FINITE DIFFERENCE METHOD FOR SOLVING THE NONLINEAR DYNAMIC EQUATION OF UNDERWATER TOWED SYSTEM

2014 ◽  
Vol 11 (04) ◽  
pp. 1350060 ◽  
Author(s):  
ZHIJIANG YUAN ◽  
LIANGAN JIN ◽  
WEI CHI ◽  
HENGDOU TIAN
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Solution ◽  
Difference Method ◽  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Computational Time ◽  
Algebraic Equations ◽  
Nonlinear Dynamic Equation ◽  
Nonlinear Dynamic Equations

A wide body of work exists that describes numerical solution for the nonlinear system of underwater towed system. Many researchers usually divide the tow cable with less number elements for the consideration of computational time. However, this type of installation affects the accuracy of the numerical solution. In this paper, a newly finite difference method for solving the nonlinear dynamic equations of the towed system is developed. The mathematical model of tow cable and towed body are both discretized to nonlinear algebraic equations by center finite difference method. A newly discipline for formulating the nonlinear equations and Jacobian matrix of towed system are proposed. We can solve the nonlinear dynamic equation of underwater towed system quickly by using this discipline, when the size of number elements is large.

scholarly journals Kamenev-Type Oscillation Criteria for the Second-Order Nonlinear Dynamic Equations with Damping on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
M. Tamer Şenel
Keyword(s):  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Sufficient Conditions ◽  
Second Order ◽  
Oscillatory Solutions ◽  
Oscillation Criteria ◽  
Nonlinear Dynamic Equation ◽  
Nonlinear Dynamic Equations ◽  
Generalized Riccati Transformation ◽  
Type Oscillation

The oscillation of solutions of the second-order nonlinear dynamic equation(r(t)(xΔ(t))γ)Δ+p(t)(xΔ(t))γ+f(t,x(g(t)))=0, with damping on an arbitrary time scaleT, is investigated. The generalized Riccati transformation is applied for the study of the Kamenev-type oscillation criteria for this nonlinear dynamic equation. Several new sufficient conditions for oscillatory solutions of this equation are obtained.

scholarly journals Oscillation Criteria for Functional Dynamic Equations with Nonlinearities Given by Riemann-Stieltjes Integral

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yuangong Sun ◽  
Taher S. Hassan
Keyword(s):  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Second Order ◽  
Dynamic Equations ◽  
Stieltjes Integral ◽  
Oscillation Criteria ◽  
Nonlinear Dynamic Equation ◽  
Nonlinear Dynamic Equations

We present new oscillation criteria for the second order nonlinear dynamic equation[r(t)ϕγ(xΔ(t))]Δ+q0(t)ϕγ(x(g0(t)))+∫ab‍q(t,s)ϕα(s)(x(g(t,s)))Δζ(s)=0under mild assumptions. Our results generalize and improve some known results for oscillation of second order nonlinear dynamic equations. Several examples are worked out to illustrate the main results.

Stability of uniform electronic wavepackets in chains and fullerenes

2015 ◽  
Vol 26 (12) ◽  
pp. 1550133 ◽  
Author(s):  
Valdemir L. Chaves Filho ◽  
Rodrigo P. A. Lima ◽  
F. A. B. F. de Moura ◽  
Marcelo L. Lyra
Keyword(s):  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Modulational Instability ◽  
The Other ◽  
Nonlinear Coupling ◽  
Phonon Coupling ◽  
Instability Analysis ◽  
Nonlinear Dynamic Equation ◽  
Electron Phonon Coupling ◽  
The Stability

In this paper, we investigate the influence of electron-lattice interaction on the stability of uniform electronic wavepackets on chains as well as on several types of fullerenes. We will use an effective nonlinear Schrödinger equation to mimic the electron–phonon coupling in these topologies. By numerically solving the nonlinear dynamic equation for an initially uniform electronic wavepacket, we show that the critical nonlinear coupling above which it becomes unstable continuously decreases with the chain size. On the other hand, the critical nonlinear strength saturates on a finite value in large fullerene buckyballs. We also provide analytical arguments to support these findings based on a modulational instability analysis.

scholarly journals On Hyers–Ulam and Hyers–Ulam–Rassias Stability of a Nonlinear Second-Order Dynamic Equation on Time Scales

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1507
Author(s):  
Alaa E. Hamza ◽  
Maryam A. Alghamdi ◽  
Mymonah S. Alharbi
Keyword(s):  
Time Scales ◽  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Sufficient Conditions ◽  
Second Order ◽  
Nonlinear Dynamic Equation ◽  
Theoretical Results ◽  
Rassias Stability

In this paper, we obtain sufficient conditions for Hyers–Ulam and Hyers–Ulam–Rassias stability of an abstract second–order nonlinear dynamic equation on bounded time scales. An illustrative example is given to show the applicability of the theoretical results.

scholarly journals Impacts of Backlash on Nonlinear Dynamic Characteristic of Encased Differential Planetary Gear Train

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Zengbao Zhu ◽  
Longchao Cheng ◽  
Rui Xu ◽  
Rupeng Zhu
Keyword(s):  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Planetary Gear ◽  
Gear Train ◽  
Planetary Gear Train ◽  
Gear Teeth ◽  
Nonlinear Dynamic Equation ◽  
Motion State ◽  
Nonlinear Dynamic Characteristic ◽  
The Impact

A multifreedom tensional nonlinear dynamic equation of encased differential planetary gear train with multibacklash and time-varying mesh stiffness was developed in the present research. The nonlinear dynamic response was obtained by solving the formulated nonlinear dynamic equation, and the impacts of backlash on dynamic characteristics of the gear train were then analyzed by combining time process diagram, phase diagram, and Poincaré section. The results revealed that bilateral shock in meshing teeth was caused due to smaller backlash, thus causing dramatic changes in meshing force; hence, the gears were found to be in a chaotic state. Further, during stable motion state, no contact between intermeshing teeth with bigger backlash was noticed; thus, they were in a stable quasiperiodic motion state in the absence of teeth exciting force. Therefore, in order to avoid a bilateral shock in gears as well as to maintain gear teeth lubrication, a slightly bigger backlash is required. The backlash change in any transmission stage caused significant impacts on gear force and the motion state of its own stage; however, the impact on gear force of another stage was quite small, whereas the impact on the motion state of another stage was quite large.

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